(4z-10)(z)=90

Solution for (4z-10)(z)=90 equation:

(4z-10)(z)=90

We move all terms to the left:

(4z-10)(z)-(90)=0

We multiply parentheses

4z^2-10z-90=0

a = 4; b = -10; c = -90;
Δ = b2-4ac
Δ = -102-4·4·(-90)
Δ = 1540
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{385}}{2*4}=\frac{10-2\sqrt{385}}{8}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{385}}{2*4}=\frac{10+2\sqrt{385}}{8}
$